Jüngel, A., López, J. L., & Montejo-Gámez, J. (2011). A New Derivation of the Quantum Navier–Stokes Equations in the Wigner–Fokker–Planck Approach. Journal of Statistical Physics, 145(6), 1661–1673. https://doi.org/10.1007/s10955-011-0388-3
moment method; Mathematical Physics; Statistical and Nonlinear Physics; Wigner-Fokker-Planck equation; osmotic momentum
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Abstract:
Siehe englisches Abstract.
de
A quantum Navier-Stokes system for the particle, momentum, and energy densities
is formally derived from the Wigner-Fokker-Planck equation using a moment method.
The viscosity term depends on the particle density with a shear viscosity coefficient which
equals the quantum diffusion coefficient of the Fokker-Planck collision operator. The main
idea of the derivation is the use of a so-called osmotic momentum operator, which is the
sum of the phase-space momentum and the gradient operator. In this way, a Chapman-
Enskog expansion of the Wigner function, which typically leads to viscous approximations,
is avoided. Moreover, we show that the osmotic momentum emerges from local gauge theory.
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Research Areas:
Quantum Modelling and Simulation: 30% Modelling and Simulation: 70%
